Solve for $x$ : $ 8|x - 6| + 10 = -6|x - 6| + 5 $
Explanation: Add $ {6|x - 6|} $ to both sides: $ \begin{eqnarray} 8|x - 6| + 10 &=& -6|x - 6| + 5 \\ \\ { + 6|x - 6|} && { + 6|x - 6|} \\ \\ 14|x - 6| + 10 &=& 5 \end{eqnarray} $ Subtract ${10}$ from both sides: $ \begin{eqnarray} 14|x - 6| + 10 &=& 5 \\ \\ { - 10} &=& { - 10} \\ \\ 14|x - 6| &=& -5 \end{eqnarray} $ Divide both sides by ${14}$ $ \dfrac{14|x - 6|} {{14}} = \dfrac{-5} {{14}} $ Simplify: $ |x - 6| = -\dfrac{5}{14}$ The absolute value cannot be negative. Therefore, there is no solution.